College Algebra (10th Edition)

by
Sullivan, Michael

Answer

$x=\ln{1.25}-1 $

Work Step by Step

Divide by 4 on both sides of the equation to obtain:
$\dfrac{4e^{x+1}}{4} = \dfrac{5}{4}
\\e^{x+1}=1.25$
Take the natural logarithm of both sides to obtain:
$\ln{(e^{x+1})}=\ln{1.25}$
Note that $\ln{(e^x)} = x$. Thus, the equation above is equivalent to:
$x+1=\ln{1.25}$
Subtract by $1$ on both sides of the equation to obtain:
$x+1-1=\ln{1.25}-1
\\x=\ln{1.25}-1 $